For Average Wall tubes the average measured wall thickness of the tube should roughly match the nominal thickness, so no need to adjust your HTRI input.
For Minimum Wall tubes the average measured wall thickness is typically around 10% thicker than the nominal thickness, so the tube ID will be smaller and you need to account for this in your HTRI input. Typically this is accomplished by increasing the tube wall thickness by 1 BWG (e.g. specify 13 BWG in HTRI for 14 BWG Minimum Wall tubes. Remember that the pressure drop through a tube is inversely proportional to the tube ID to the 5th power, so a 10% difference in the ID can have a substantial impact on the pressure drop.
Keep in mind that everything I've written above is for welded tubes (since seamless tubes are drawn over a mandrel I don't think the wall thickness tolerance actually effects the measured ID?) and assumes that there won't ever be any fouling deposits on the tube ID.
-Christine